IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v137y2020ics0960077920302393.html
   My bibliography  Save this article

Simplicial degree in complex networks. Applications of topological data analysis to network science

Author

Listed:
  • Hernández Serrano, Daniel
  • Hernández-Serrano, Juan
  • Sánchez Gómez, Darío

Abstract

Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among more than two agents, having thus an inherent structure of a simplicial complex. The relevance of an agent in a graph network is given in terms of its degree, and in a simplicial network there are already notions of adjacency and degree for simplices that, as far as we know, are not valid for comparing simplices in different dimensions. We propose new notions of higher-order degrees of adjacency for simplices in a simplicial complex, allowing any dimensional comparison among them and their faces. We introduce multi-parameter boundary and coboundary operators in an oriented simplicial complex and also a novel multi-combinatorial Laplacian is defined. As for the graph or combinatorial Laplacian, the multi-combinatorial Laplacian is shown to be an effective tool for calculating the higher-order degrees presented here. To illustrate the potential applications of these theoretical results, we perform a structural analysis of higher-order connectivity in simplicial-complex networks by studying the associated distributions with these simplicial degrees in 17 real-world datasets coming from different domains such as coauthor networks, cosponsoring Congress bills, contacts in schools, drug abuse warning networks, e-mail networks or publications and users in online forums. We find rich and diverse higher-order connectivity structures and observe that datasets of the same type reflect similar higher-order collaboration patterns. Furthermore, we show that if we use what we have called the maximal simplicial degree (which counts the distinct maximal communities in which our simplex and all its strict sub-communities are contained), then its degree distribution is, in general, surprisingly different from the classical node degree distribution.

Suggested Citation

  • Hernández Serrano, Daniel & Hernández-Serrano, Juan & Sánchez Gómez, Darío, 2020. "Simplicial degree in complex networks. Applications of topological data analysis to network science," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
  • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920302393
    DOI: 10.1016/j.chaos.2020.109839
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920302393
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2020.109839?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hernández Serrano, Daniel & Sánchez Gómez, Darío, 2020. "Centrality measures in simplicial complexes: Applications of topological data analysis to network science," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    2. Maletić, Slobodan & Rajković, Milan, 2014. "Consensus formation on a simplicial complex of opinions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 111-120.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Feng, Meiling & Li, Xuezhu & Zhao, Dawei & Xia, Chengyi, 2023. "Evolutionary dynamics with the second-order reputation in the networked N-player trust game," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    2. Serrano, Daniel Hernández & Villarroel, Javier & Hernández-Serrano, Juan & Tocino, Ángel, 2023. "Stochastic simplicial contagion model," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    3. Xiong, Kezhao & Zhou, Man & Liu, Wei & Zhang, Xiyun, 2024. "Regulating thermal rectification on random networks by depositing nanoparticles," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sudhamayee, K. & Krishna, M. Gopal & Manimaran, P., 2023. "Simplicial network analysis on EEG signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    2. Andjelković, Miroslav & Tadić, Bosiljka & Maletić, Slobodan & Rajković, Milan, 2015. "Hierarchical sequencing of online social graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 582-595.
    3. Václav Snášel & Pavla Dráždilová & Jan Platoš, 2021. "Cliques Are Bricks for k-CT Graphs," Mathematics, MDPI, vol. 9(11), pages 1-9, May.
    4. Li Ding & Ping Hu, 2019. "Contagion Processes on Time-Varying Networks with Homophily-Driven Group Interactions," Complexity, Hindawi, vol. 2019, pages 1-13, October.
    5. Serrano, Daniel Hernández & Villarroel, Javier & Hernández-Serrano, Juan & Tocino, Ángel, 2023. "Stochastic simplicial contagion model," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    6. Hernández Serrano, Daniel & Sánchez Gómez, Darío, 2020. "Centrality measures in simplicial complexes: Applications of topological data analysis to network science," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    7. Shang, Yilun, 2022. "Sombor index and degree-related properties of simplicial networks," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    8. Kovalenko, K. & Romance, M. & Vasilyeva, E. & Aleja, D. & Criado, R. & Musatov, D. & Raigorodskii, A.M. & Flores, J. & Samoylenko, I. & Alfaro-Bittner, K. & Perc, M. & Boccaletti, S., 2022. "Vector centrality in hypergraphs," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920302393. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.